The weekly revenue for a product is given by R(x) = 324x - 0.0495x?, and the weekly cost is C(x) = 8000 + 162x - 0.099x2 + 0.00003x”, where x is the number of units
produced and sold
(a) How many units will give the maximum profit?
(b) What is the maximum possible profit?
(a) The number of units that will give the maximum profit is
(Round to the nearest whole number as needed.)

Answer:

(a) The number of units that will give the maximum profit is 2,000 units.

(b) The maximum possible profit is $274,000.

Step-by-step explanation:

(a) How many units will give the maximum profit?

From the attached photo in the question, we are given;

R(x) = 324x - 0.0495x^2 ………………....................................……….. (1)

C(x) = 8000 + 162x - 0.099x^2 + 0.00003x^3 …………………….. (2)

In economics, profit function, P(x), is obtained as follows:

P(x) = R(x) - C(x) ………………………. (3)

Substituting the equations (1) and (2) for R(x) and C(x) respectively into equation (3) and then simplify, we have:

P = 324x - 0.0495x^2 - (8000 + 162x - 0.099x^2 + 0.00003x^3)

P = 324x - 0.0495x^2 - 8000 - 162x + 0.099x^2 - 0.00003x^3

P = -8000 + 162x + 0.0495x^2 - 0.00003x^3 ………………….. (4)

Taking a derivative of equation (4) with respect to x and equating to 0, we have:

162 + 0.099x - 0.00009x^2 = 0 .................... (5)

Using the almighty formula as follows:

x = (-b +/- (b^2 - 4ac)^0.5) / 2a ………………. (6)

Where, from equation (5);

a = - 0.00009

b = 0.099

c = 162

Substituting the values into equation (6), we have:

x = (-0.099 +/- (0.099^2 - (4 * (- 0.00009) * 162))^0.5) / (2 * - 0.00009)

x = (-0.099 +/- 0.261) / -0.00018

x = (-0.099 + 0.261) / -0.00018, or x = (-0.099 - 0.261) / -0.00018

x = -900, or x = 2000

Since negative number does not have economic value in economics, the number of units that will give the maximum profit is therefore 2,000 units.

(b) What is the maximum possible profit?

From part a, x = 2000

Substituting x = 2000 into equation (4) and then solve, we have:

P(x) = -8000 + (162 * 2000) + (0.0495 * 2000^2) - (0.00003 * 2000^3)

P(x) = 274,000

Therefore, the maximum possible profit is $274,000.

Sending Paypal to whoever gets this right ( i made this question)

HELPPP ASAP!!!!!!! PLZZZ​

Pllzzzzzzz help now it’s due today

There is a line that includes the point (2, 10) and has a slope of 1. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Submit

Answer Please : )
Why negative ( - ) sign is cannot be pulled out of square root.???​

A music club has 35 drum players. If 25% of the total number of members in the club are drum players, what is the total number of member in the club?

What are fractions? Plz help

how many solutions does this problem have: 2(75 + 8) = 5(85 + 9)​

The first equation from the system of equations is graphed. Graph the second equation to find the solution of the system of equations. y = –x, y = 2x + 6 What is the point of intersection? (2, 1) (–1, 2) (0, 6) (–2, 2)

#1 Identify the characteristics of the quadratic graph
Vertex:
у
Axis of symmetry:
Domain:
Range:
Increase Interval:
Decrease Interval:

What is the equation of the line that passes through the point (-5,0) and has a
slope of 3/5

Quick please

A student put $1,200 in a savings account paying simple interest of 4.5% per year. Find the total amount of the student's savings after 5 years. A: $700. B: $1470. C: $1000. D: $400​

which one is the missing proof?

What is 77/20 simplified

7) What is the equation of a circle with the center (-8, 9) and the radius of 10?​

please answer correctly!!

This is for Geometry.
If it is blurry Zoom in.
Please helps me, Thx!

Bob's average golf score at his local course is 93.6 from a random sample of 34 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The 90% confidence interval around this sample mean is:_______.
a. (92.4, 94.8).
b. (89.0, 98.3).
c. (90.5, 96.7).
d. (93.2, 94.0).

someone help me on this question
it's two step inequalities
i forgot how to do this​

an elevator can carry 800 of weight. A football player weighting 280 pounds gets on the elevator with a student. Write and solve an inequality to represent the remaining weight that can be added.

Hiking
(15,18
(10, 12)
Distance (miles)
15,6
10
15
Time
Using the data shown on the graph, which sztements are correct?
The
3
The ratio of L is consistent
The graph represents a proportional relationship
D
The grach does not represent a proportional relationship
The graph of a proportional relationship must past through. (0,0)

Use vector operations to draw the resultant vector

U
Question 9
10 pts
Solve this system of equations using substitution algebraically. Check your answer using
substitution.
3x + 4y = 36
y= x+8

-3 3/4+ 1/2 please help

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.

Graph of two intersecting lines. The line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded below the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded below the line.

The graph represents which system of inequalities?

y ≤ −3x − 1
y ≤ −x − 4
y > −3x + 1
y ≤ −x − 4
y < 3x − 1
y ≤ −x + 4
y ≤ 3x − 1
y ≥ −x + 4

WILL MARK BRAINLYEST

What is the equation in point-slope form of the line that passes through the points (7, 5) and (-4, – 1)?

The ratio of cars to trucks in the parking lot is 3:5. If there are 360 vehicles in the parking lot, how
may are trucks?

Someone please help me

Is AB congruent to CB?

A parallelogram is transformed according to the rule (x, y) - (x. y). Which is another way to state the
transformation?
O R0 90 degrees
O R0 180 degrees
O R0 270 degrees
O R0 360 degrees